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Contents

1. Significant Wave Height(Hs)

2. Zero Crossing Wave Period(Tz)

3. PM Spectrum4. Jonswap Spectra

5. Airys Wave Theory

6. Stokes 5th order Wave calculation

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Significant Wave

Height is the averageof top 1/3rdwaves

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y Significant wave height represented as Hs or Hsig orH1/3.y Important level when considering the statistical

distribution of ocean waves.

PROCEDURE TO FIND OUT H1/3

1. select a random wave profile .

2.arrange in descending order.

3. choose top 1/3rd & find Avg.

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Zero Crossing Wave Period (Tz, Tav)

1.The average timeinterval between similar

direction crossings ofmean water level for a

wave record

2.The zero crossing period canalso be calculated from themoments of wave frequency

spectra. Tz = square root

of(m0/m2).

3.Also called the MeanSpectral Period.

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PM spectrum:Defines the Pierson Moskowitz spectra in the

wave-frequency domain.

y The Pierson-Moskowitz (PM) spectra is an empirical

relationship that defines the distribution of energywith frequency within the ocean.

y PM spectrum is one of the simplest descriptions forthe energy distribution

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Defines the Pierson Moskowitz spectra in the wave-frequency domain.

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Theequationis:

yWhere

is the wind speed at 19.5m above the sea surface.

y

Parametersw=wave-frequency (2 /s)

wp=the peak wave frequency (2 /s)

alpha=The intensity of the Spectra. Default value (0.0081)

beta=A shape factor. Default value = 1.25

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The JONSWAP spectra in the wave-frequency

domain:

y The JONSWAP (Joint North Sea Wave Project) spectra is anempirical relationship that defines distribution of energywith frequency within the ocean.

y The underlying equation is:

Where:

, &

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y PARAMETER:y W

=wave-frequency (2 /s)y Wp=the peak wave frequency (2 /s)

y Alpha=The intensity of the Spectra. Default value = 0.0081

y Gamma=Peak enhancement factor. Default value = 3.3

y Beta=A shape factor (Rarely changed). Default value = 1.25

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Airys wavetheory:y It is a linear theory for the propagation of waves on the

surface of a potential flow & above a horizontal bottom

y

The free surface elevation (x,t) of one wavecomponent issinusoidal:

yAs a function of horizontal position xand time t:

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yWhere:

y a is the wave amplitude in metre,

y cos is the cosine function,y kis the angular wavenumber in radian per metre,

related to thewavelength as

y is the angular frequencyin radian per second:

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Stokes 5th orderwave calculation:y The wavelength L and the Stokes lamda parameter are calculated by

solving

y = H / ( L ( ( B35 + B55 ) 4 + B33 2 + 1 ) )

y L = Lo tanh( 2 d / L )( C2 4 + C1 2 + 1 )

y Where

= Stokes lamda Coefficient

L = Ocean Wave Length

Lo = Deep Water Wave Length = ( 9.80665 T2) / ( 2 )

B33, B35, B55, C1 and C2 are coefficients dependant on L

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Stokes fifth orderwave calculators.

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